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$Simplify. ((17×2^(4)×5^(3)+10^(3)÷5+2^(3)×5+2^(2)×11)×5^(5)×4^(2)×2+2^(7)×5^(2)+root(3)(64)+2^(5)×5^(4))/((5^(3)×2^(2)×sqrt4)-{(2^(4)×3÷2)÷2}×(2^(4)×5+3))×11$

Simplify. $\newline$ $\frac{\left(17 \times 2^{4} \times 5^{3}+10^{3} \div 5+2^{3} \times 5+2^{2} \times 11\right) \times 5^{5} \times 4^{2} \times 2+2^{7} \times 5^{2}+\sqrt[3]{64}+2^{5} \times 5^{4}}{\left(5^{3} \times 2^{2} \times \sqrt{4}\right)-\left\{\left(2^{4} \times 3 \div 2\right) \div 2\right\} \times\left(2^{4} \times 5+3\right)} \times 11$

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Calculus

Find derivatives of using multiple formulae

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Q. Simplify.

\newline

\frac{\left(17 \times 2^{4} \times 5^{3}+10^{3} \div 5+2^{3} \times 5+2^{2} \times 11\right) \times 5^{5} \times 4^{2} \times 2+2^{7} \times 5^{2}+\sqrt[3]{64}+2^{5} \times 5^{4}}{\left(5^{3} \times 2^{2} \times \sqrt{4}\right)-\left\{\left(2^{4} \times 3 \div 2\right) \div 2\right\} \times\left(2^{4} \times 5+3\right)} \times 11

Simplify Numerator: First, simplify the terms inside the parentheses in the numerator. $\newline$ ((\(17\times $2$ ^{ $4$ }\times $5$ ^{ $3$ }+ $10$ ^{ $3$ }\div $5$ + $2$ ^{ $3$ }\times $5$ + $2$ ^{ $2$ }\times $11$ )\times $5$ ^{ $5$ }\times $4$ ^{ $2$ }\times $2$ + $2$ ^{ $7$ }\times $5$ ^{ $2$ }+\sqrt[ $3$ ]{ $64$ }+ $2$ ^{ $5$ }\times $5$ ^{ $4$ }) $\newline$ = (( $17$ \times $16$ \times $125$ + $1000$ \div $5$ + $8$ \times $5$ + $4$ \times $11$ )\times $3125$ \times $16$ \times $2$ + $128$ \times $25$ + $4$ + $32$ \times $625$ )
Calculate Simplified Terms: Now, calculate the simplified terms. $\newline$ = $((27200+200+40+44)\times3125\times32+3200+4+20000)$ $\newline$ = $(27484\times3125\times32+3200+4+20000)$
Multiply Terms: Multiply the terms together. $\newline$ = $(27484\times100000+3200+4+20000)$ $\newline$ = $2748400000+3200+4+20000$
Add Remaining Terms: Add the remaining terms. $\newline$ $= 2748400000+3200+4+20000$ $\newline$ $= 2748432204$
Simplify Denominator: Now, simplify the denominator. $\newline$ ((\(5^{ $3$ }\times $2$ ^{ $2$ }\times\sqrt{ $4$ })-{( $2$ ^{ $4$ }\times $3$ \div $2$ )\div $2$ }\times( $2$ ^{ $4$ }\times $5$ + $3$ )) $\newline$ = (( $125$ \times $4$ \times $2$ )-( $16$ \times $3$ \div $2$ )\div $2$ \times( $16$ \times $5$ + $3$ )) $\newline$ = ( $1000$ $-24$ \div $2$ \times( $80$ + $3$ ))
Calculate Simplified Terms: Calculate the simplified terms in the denominator. $\newline$ = $(1000-12\times83)$ $\newline$ = $(1000-996)$
Subtract Terms: Subtract the terms. $\newline$ = $1000-996$ $\newline$ = $4$
Divide and Multiply: Divide the numerator by the denominator and multiply by $11$ . $\newline$ = $2748432204 \div 4 \times 11$ $\newline$ = $687108051 \times 11$
Final Answer: Multiply to get the final answer. $\newline$ = $687108051\times11$ $\newline$ = $7558188561$